Question

Find the product of (3x-5)(4x+7)

Answer 1

The product of (3x-5)(4x+7) is

`12x^2+x-35`

SOLUTION

Problem Statement

The question asks us to find the following product:

`(3x-5)(4x+7)`

Method

To solve this question, we need to apply the FOIL Method. The FOIL method is given below:

The diagram shows how to apply the FOIL method.

- First (F) - Multiply the first numbers from both brackets

- Outside (O) - Multiply the two outer values of both brackets i.e. the first value in the first bracket on the left and the last value on the second bracket on the right.

- Inside (I) - Multiply the two inner values of both brackets i.e. the second value in the first bracket and the first value in the second bracket. This is also the same as saying we multiply the middle values

- Last (L) - Multiply the last numbers in both brackets

After performing this multiplication, we add up the result.

Implementation

The product is thus computed below:

`\begin{gathered} (3x-5)(4x+7) \\ \text{Applying the FOIL method:} \\ F-\text{First:} \\ 3x*4x=12x^2 \\ \\ O-\text{Outside:} \\ 3x*7=21x \\ \\ I-\text{Inside:} \\ -5*4x=-20x \\ \\ L-\text{Last:} \\ -5*7=-35 \\ \\ \text{Adding up the results, we have:} \\ 12x^2+21x-20x-35 \\ =12x^2+x-35 \\ \\ \therefore(3x-5)(4x+7)=12x^2+x-35 \end{gathered}`

Final Answer

The product of (3x-5)(4x+7) is

`12x^2+x-35`